Tutorial Multiphaseriet
Multiphase Rietveld Refinement
Files needed: d5_05628.raw, wo3.cif, y2o3.cif, si.cif
Learning Outcomes: This example shows a simple multiphase Rietveld refinement using laboratory data. It’s a slightly artificial example that we use for training students on qualitative phase identification in Durham. Rietveld refinement allows you to attempt quantitative analysis on the same data set. Beware: don’t trust the absolute numbers unless you’re working very carefully and have performed all the necessary data corrections and independent calibrations! In this case the samples were taken “from the bottle” with no special care taken over the sample preparation and data collection. The significant absorption differences between WO3 and Si and preferred orientation will affect the quantitative results.
Topas advantages: quick, easy and robust; phases can be refined independently or parameters linked between phases in a straightforward manner.
1. Save the datafile and cif files in your working directory.
2. The input file can be set up in exactly the same way as a single phase Rietveld refinement, you just have to load in 3 cif files – one for each phase. Follow the TOPAS_Durham menus for a Rietveld refinement. Select data file d5_05628, select diffractometer BB_CuKa2_graphite_scint. Fixed slits were used. In Corrections, refine the sample height.
3. In the Rietveld or Pawley section click on “Structure from CIF” three times. First time read in Y2O3.cif, then WO3.cif, then Si.CIF.
4. You should notice that each time you read in a CIF the “for strs” section is moved to the end of the file. Parameter names and the CIF_PHASE_ID are also automatically numbered for each str. The “for strs” section contains information that is applied to each of the strs.
5. Warning: parameters in a “for strs” or “for xdds” section must be given names (not @). This is so TOPAS refines and stores a single value. If you use the “@” symbol, parameters in “for strs” will refine to different values for each str, but only one value will be stored in the INP file. Always check that the number of refined parameters reported by TOPAS (in the fit window or log file) is what you expect.
6. Send the file to TOPAS and do a default refinement. You should get Rwp = 24.1%.
7. Try refining the cell parameter of each phase. Remember to give a/b/c identical parameter names for the cubic Y2O3/Si; don’t refine alpha/gamma for monoclinic WO3. You should get Rwp ~20.4%.
8. Refine a single overall temperature factor for each site. Immediately before the first structure define a parameter with “prm b_overall 0.0.5”. At the end of each site define the isotropic displacement parameter with “beq = b_overall;:0”. The “:0” means the refined single value will get reported in the INP at the end of the refinement. You should now get Rwp ~17.2%.
9. Look at the fit. It’s clear that the single overall peakshape being used for each str from the for_strs section isn’t modelling peaks shapes very well. Try giving each phase a different set of peakshape parameters. One approach is to assume that Si is the most crystalline phase with the sharpest peaks and can be used to define the instrumental resolution function. The additional broadening in the Y2O3 and WO3 phases can then be described with terms relating to crystallite size and microstrain. For the Y2O3 and WO3 phases uncomment the lines below:
'LVol_FWHM_CS_G_L(1, 100, 0.89, 100, csgc1, 100, cslc1, 100)
'e0_from_Strain( 0.001, sgc1, 0.001, slc1, 0.001)
The quantitative meaning of these macros is explored in tutorials on size/strain. In this tutorial we will use them empirically. The refineable terms csgc1 and cslc1 describe “crystallite size gaussian contribution for phase 1” and “crystallite size lorentzian contribution for phase”. sgc1 and slc1 are “strain gaussian contribution phase 1” and “strain lorentzian contribution phase 1”.
10. With this model you should get Rwp ~14.9%.
11. Instead of using the TCHZ description you could use a size/strain description for all strs. Put a comment in front of the TCHZ peak shape in the “for strs” section. Uncomment the size/strain lines for Si. You should get Rwp ~14.5 %. A better approach might be to fix the parameters of the TCHZ function at values derived from a highly crystalline standard like CeO2 so that it describes the instrument resolution function (see other tutorials).
12. Look at the fit. There is a significant misfit on the Si 111 reflection which could imply preferred orientation. Add the line “Preferred_Orientation(@, 0.5,, 1 1 1)” below the site line for Si. You should see an improved fit with Rwp ~12.1% with a Si weight percent of ~58% in the TOPAS window (go to View and make sure “Phase Names” and “hkl ticks” are ticked if you don’t see it).
13. Turn on do_errors in the file and look at the correlation matrix. You will see high correlations between the size/strain terms for each str (values >>90%). This suggests that the model has parameters which are not needed to fit the data. For each of the strs have a look at the size and strain parameters. If a size is large (>>100) or strain is small (<<0.01) then it’s probably not contributing to the peak shape and the contribution can be removed from the model. For size set the value to 9999 for “infinite size”. For strain stet the value to 0.0001 for “zero strain”. For Y2O3 you can probaly do this for !sgc1 and !slc1. For WO3 !slc2. For Si !sgc3. Turning off these parameters gave Rwp ~12.1%, essentially unchanged.
14. In TOPAS this approach of turning multiple parameters on, seeing the quality of the fit then turning parameters off sequentially normally works. It wouldn’t work in other software. You will sometimes find that Rwp can be lower with fewer parameters, implying that the correlations when using too many parameters are affecting the least squares miniminsation.
15. The quantitative analysis in this example will not be reliable for the reasons given in the introduction. However you can get some feeling for how the parameters of the model affect quantitative wt % values. The Si wt % in this model is 58.2%. Try turning off the Si preferred orientation correction; the value will change to ~62%. Try turning preferred orienation back on and using a different temperature factor for each phase. The wt % again changes to ~62%.
16. In case you mess up try the file linked here.